Processing data base information having nonwhite noise

ABSTRACT

A method and system for processing a set of data from an industrial process and/or a sensor. The method and system can include processing data from either real or calculated data related to an industrial process variable. One of the data sets can be an artificial signal data set generated by an autoregressive moving average technique. After obtaining two data sets associated with one physical variable, a difference function data set is obtained by determining the arithmetic difference between the two pairs of data sets over time. A frequency domain transformation is made of the difference function data set to obtain Fourier modes describing a composite function data set. A residual function data set is obtained by subtracting the composite function data set from the difference function data set and the residual function data set (free of nonwhite noise) is analyzed by a statistical probability ratio test to provide a validated data base.

This application is a continuation-in-part of U.S. Ser. No. 07/827,776,filed Jan. 29, 1992 now U.S. Pat. No. 5,223,207.

The United States Government has rights in this invention pursuant toContract W-31-109-ENG-38 between the U.S. Department of Energy and theUniversity of Chicago.

The present invention is concerned generally with a system and methodfor reliably processing a data base of information having nonwhite noisecharacteristics. More particularly, the invention is concerned with asystem and method for removal of nonwhite noise elements, such asserially correlated noise, from an incoming steam of data or from anexisting data base. This method allows use of reliable data, orproviding a validated data set, from an industrial process and/orsensors which monitor the process. Such a system further allowsaccumulation of characteristic faulty data arising from nonwhite noisewhich can be useful in understanding the varieties and characteristicsof noise which cause false alarm conditions.

Conventional parameter-surveillance schemes are sensitive only to grosschanges in the mean value of a process, or to large steps or spikes thatexceed some threshold limit check. These conventional methods can passthrough data containing bad information characterized by large numbersof false alarms (if thresholds are set too close to normal operatinglevels) or a large number of missed (or delayed) alarms (if thethresholds are set too expansively). Such a system gives rise to afaulted data base of information for researchers or for engineersanalyzing the status of an industrial process. Moreover, mostconventional methods cannot perceive the onset of a process disturbanceor sensor deviation which gives rise to a signal below the thresholdlevel for an alarm condition.

In another conventional monitoring method, the Sequential ProbabilityRatio Test ("SPRT") has found wide application as a signal validationtool in the nuclear reactor industry. Two features of the SPRT techniquemake it attractive for parameter surveillance and fault detection: (1)early annunciation of the onset of a disturbance in noisy processvariables, and (2) the SPRT technique has user-specifiable false-alarmand missed-alarm probabilities. One important drawback of the SPRTtechnique that has limited its adaptation to a broader range of nuclearapplications is the fact that its mathematical formalism is founded uponan assumption that the signals it is monitoring are purely Gaussian,independent (white noise) random variables.

It is therefore an object of the invention to provide an improved methodand system for processing data base information having nonwhite noisepresent.

It is another object of the invention to provide a novel method andsystem for statistically filtering industrial process signals havingvirtually any form of noise signal.

It is a further object of the invention to provide an improved methodand system for operating on an industrial process signal data base toremove unwanted serially correlated noise signals.

It is still an additional object of the invention to provide a novelmethod and system utilizing a data base formed from a pair of signals togenerate a difference function to be analyzed for anomalous data.

It is still a further object of the invention to provide an improvedmethod and system for collecting a reliable data base from at least onesensor for providing a real signal characteristic of a process and apredicted sensor signal allowing formation of a difference signalbetween the predicted and real signal for subsequent analysis andaccumulation of data free from nonwhite noise contamination.

It is also an object of the invention to provide a novel method andsystem wherein a difference function is formed from a data base of twosensor signals, and/or pairs of signals and nonwhite noise is removedenabling collection of reliable data.

It is yet an additional object of the invention to provide an improvedmethod and system utilizing variable pairs of sensors for accumulatingreliable data both for sensor degradation and industrial processes.

Other objects, features and advantages of the present invention will bereadily apparent from the following description of the preferredembodiments thereof, taken in conjunction with the accompanying drawingsdescribed below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the specified output of a pump's power output overtime;

FIG. 2 shows a Fourier composite curve fit to the pump spectral outputof FIG. 1;

FIG. 3 illustrates a residual function characteristic of the differencebetween FIGS. 1 and 2;

FIG. 4A shows a periodogram of the spectral data of FIG. 1 and FIG. 4Bshows a periodogram of the residual function of FIG. 3;

FIG. 5A illustrates a noise histogram for the pump power output of FIG.1 and FIG. 5B illustrates a noise histogram for the residual function ofFIG. 3;

FIG. 6A shows an unmodified delayed neutron detector signal from a firstsensor and FIG. 6B is for a second neutron sensor; FIG. 6C shows adifference function characteristic of the difference between data inFIG. 6A and 6B and FIG. 6D shows the data output from a SPRT analysiswith alarm conditions indicated by the diamond symbols;

FIG. 7A illustrates an unmodified delayed neutron detector signal from afirst sensor and FIG. 7B is for a second neutron sensor; FIG. 7C shows adifference function for the difference between the data of FIG. 7A and7B and FIG. 7D shows the result of using the instant invention to modifythe difference function to provide data free of serially correlatednoise to the SPRT analysis to generate alarm information and with alarmconditions indicated by the diamond signals;

FIG. 8 illustrates a schematic functional flow diagram of a method ofprocessing a data stream with FIG. 8A showing a first phase of a methodof the invention and FIG. 8B shows the application of a method of theinvention;

FIG. 9 illustrates schematically the implementation of data by a methodof the invention using a DOS-type system;

FIG. 10 is similar to FIG. 9, but processes a plurality of SPRT dataanalysis modules outputting data to the data base; and

FIG. 11 illustrates an implementation of the method of the invention fora UNIX-type system.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In a method of the invention, data base information obtained fromindustrial process sensors can be used to accumulate reliable data andalso to modify or terminate degrading or anomalous processes. The methodof the invention can thus be applied to an incoming data stream toprevalidate the data or applied to an existing data base can be analyzedto remove faulty data. The data base sensor signals can therefore beused for research purposes as well as to manipulate input data to astatistical analysis technique, such as a process entitled SequentialProbability Ratio Test ("SPRT"). Details of this process and theinventions therein are disclosed in U.S. patent application Ser. No.07/827,776, now U.S. Pat No. 5,223,207, which is incorporated byreference herein in its entirety. Also see the copending applicationincorporated by reference herein, filed contemporaneously and entitled,"System for Monitoring an Industrial Process and Determining Sensor"(Ser. No. 08/068,713). The procedures followed in a preferred method areshown generally in FIG. 8. In performing such a preferred analysis ofthe sensor signals, a dual transformation method is performed, insofaras it entails both a frequency-domain transformation of the originaltime-series data and a subsequent time-domain transformation of theresultant data. The data stream that passes through the dualfrequency-domain, time-domain transformation is then processed with theSPRT procedure, which uses a log-likelihood ratio test. A computersoftware Appendix is also attached hereto covering the SPRT procedureand its implementation in the context of, and modified by, the instantinvention.

In the preferred embodiment, successive data observations are performedon a discrete process Y, which represents a comparison of the stochasticcomponents of physical processes monitored by a sensor, and mostpreferably pairs of sensors. In practice, the Y function is obtained bysimply differencing the digitized data signals from two respectivesensors. Let y_(k) represent a data sample from the process Y at timet_(k). During normal operation with an undegraded physical system andwith sensors that are functioning within specifications the y_(k) shouldbe normally distributed with mean of zero. Note that if the two datasignals being compared do not have the same nominal mean values (due,for example, to differences in calibration), then the input signals willbe pre-normalized to the same nominal mean values during initialoperation.

In performing the monitoring of industrial processes an incoming datastream can be validated or an existing data base can be validated. Thesystem's purpose is to declare data from a first system or a secondsystem degraded if the drift in Y is sufficiently large that thesequence of observations appears to be distributed about a mean +M or-M, where M is our pre-assigned system-disturbance magnitude. We wouldlike to devise a quantitative framework that enables us to decidebetween two hypotheses, namely:

H₁ : Y is drawn from a Gaussian probability distribution function "PDF")with mean M and variance σ².

H₂ : Y is drawn from a Gaussian PDF with mean 0 and variance σ².

We will suppose that if H₁ or H₂ is true, we wish to decide for H₁ or H₂with probability (1-β) or (1-α), respectively, where α and β representthe error (misidentification) probabilities.

From the conventional, well known theory of Wald, the test depends onthe likelihood ratio 1_(n), where ##EQU1##

After "n" observations have been made, the sequential probability ratiois just the product of the probability ratios for each step: ##EQU2##where f(y|H) is the distribution of the random variable y.

Wald's theory operates as follows: Continue sampling as long as A<1_(n)<B. Stop sampling and decide H₁ as soon as 1_(n) ≧B, and stop samplingand decide H₂ as soon as 1_(n) ≦A. The acceptance thresholds are relatedto the error (misidentification) probabilities by the followingexpressions: ##EQU3##

The (user specified) value of α is the probability of accepting H₁ whenH₂ is true (false alarm probability). β is the probability of acceptingH₂ when H₁ is true (missed alarm probability).

If we can assume that the random variable y_(k) is normally distributed,then the likelihood that H₁ is true (i.e., mean M, variance σ²) is givenby: ##EQU4## Similarly for H₂ (mean 0, variance σ²): ##EQU5## The ratioof (5) and (6) gives the likelihood ratio 1_(n) ##EQU6## Combining (4)and (7), and taking natural logs gives ##EQU7## Our sequential samplingand decision strategy can be concisely represented as: ##EQU8##

Following Wald's sequential analysis, it is conventional that a decisiontest based on the log likelihood ratio has an optimal property; that is,for given probabilities α and β there is no other procedure with atleast as low error probabilities or expected risk and with shorterlength average sampling time.

A primary limitation that has heretofore precluded the applicability ofWald-type binary hypothesis tests for sensor and equipment surveillancestrategies lies in the primary assumption upon which Wald's theory ispredicated; i.e., that the original process Y is strictly "white" noise,independently-distributed random data. White noise is well known to be asignal which is uncorrelated. Such white noise can, for example, includeGaussian noise. It is, however, very rare to find physical process dataassociated with operating machinery or other industrial processes thatare not contaminated with serially-correlated, deterministic noisecomponents. Serially correlated noise components are conventionallyknown to be signal data whose successive time point values are dependenton one another. Noise components include, for example, auto-correlated(also known as serially correlated) noise and Markov dependent noise.Auto-correlated noise is a known form of noise wherein pairs ofcorrelation coefficients describe the time series correlation of variousdata signal values along the time series of data. That is, the data U₁,U₂, . . . , U_(n) have correlation coefficients (U₁, U₂), (U₂, U₃), . .. , (U_(n-1), U_(n)) and likewise have correlation coefficients (U₁,U₃), (U₂, U₄ ) etc. If these data are auto-correlated, at least some ofthe coefficients are non-zero. Markov dependent noise on the other handis a very special form of correlation between past and future datasignals. Rather, given the value of U_(k), the values of U_(n), n>k, donot depend on the values of U_(j) where j<k. This implies thecorrelation pairs (U_(j), U_(n)) given the value U_(k), are all zero.If, however, the present value is imprecise, then the correlationcoefficients may be nonzero. This invention can overcome this limitationto conventional surveillance strategies by integrating the Waldsequential-test approach with a new dual transformation technique. Thissymbiotic combination of frequency-domain transformations andtime-domain transformations produces a tractable solution to aparticularly difficult problem that has plagued signal-processingspecialists for many years.

In the preferred embodiment of the method shown in detail in FIG. 8,serially-correlated data signals from an industrial process can berendered amenable to the SPRT testing methodology describedhereinbefore. This is preferably done by performing a frequency-domaintransformation of the original difference function Y. A particularlypreferred method of such a frequency transformation is accomplished bygenerating a Fourier series using a set of highest "1" number of modes.Other procedures for rendering the data amenable to SPRT methodsincludes, for example, auto regressive techniques, which can accomplishsubstantially similar results described herein for Fourier analysis. Inthe preferred approach of Fourier analysis to determine the "1" highestmodes (see FIG. 8A): ##EQU9## where a₀ /2 is the mean value of theseries, a_(m) and b_(m) are the Fourier coefficients corresponding tothe Fourier frequency ω_(m), and N is the total number of observations.Using the Fourier coefficients, we next generate a composite function.X_(t), using the values of the largest harmonics identified in theFourier transformation of Y_(t). The following numerical approximationto the Fourier transform is useful in determining the Fouriercoefficients a_(m) and b_(m). Let x_(j) be the value of X_(t) at the jthtime increment. Then assuming 2π periodicity and letting ω_(m) =2πm/N,the approximation to the Fourier transform yields: ##EQU10## for0<m<N/2. Furthermore, the power spectral density ("PSD") function forthe signal is given by 1_(m) where To keep the signal bandwidth asnarrow as possible without distorting the PSD, no spectral windows orsmoothing are used in our implementation of the frequency-domaintransformation. In analysis of data from a pumping system of the EBR-IIreactor of Argonne National Laboratory (West), the Fourier modescorresponding to the eight highest 1_(m) provide the amplitudes andfrequencies contained in X_(t). In our investigations for the particularpumping system data accumulated, the highest eight 1_(m) modes werefound to give an accurate reconstruction of X_(t) while reducing most ofthe serial correlation for the physical variables studied. In otherindustrial processes, the analysis could result in more or fewer modesbeing needed to accurately construct the functional behavior of acomposite curve. Therefore, the number of modes used is a variable whichis iterated to minimize the degree of nonwhite noise for any givenapplication. As noted in FIG. 8A a variety of noise tests are applied inorder to remove serially correlated noise.

The reconstruction of X_(t) uses the general form of Eqn. (12), wherethe coefficients and frequencies employed are those associated with theeight highest PSD values. This yields a Fourier composite curve (see endof flowchart in FIG. 8A) with essentially the same correlation structureand the same mean as Y_(t). Finally, we generate a discrete residualfunction R_(t) by differencing corresponding values of Y_(t) and X_(t).This residual function, which is substantially devoid of seriallycorrelated contamination, is then processed with the SPRT techniquedescribed hereinbefore.

FIGS. 9 and 10 schematically illustrate general implementation of themethods of processing EBR-II data; in particular FIGS. 9 and 10 areimplemented on a DOS-type system that does not allow concurrentprocessing. FIG. 11 illustrates a detailed implementation on a UNIX typesystem which allows multiple concurrent processing.

In a specific example application of the above referenced methodology,certain data variables were monitored from the Argonne NationalLaboratory (West) reactor EBR-II. In particular, EBR-II reactor coolantpumps (RCPs) and delayed neutron (DN) monitoring systems were testedcontinuously to demonstrate the power and utility of the invention. TheRCP and DN systems were chosen for initial application of the approachbecause SPRT-based techniques have already been under development forboth the systems. All data used in this investigation were recordedduring full-power, steady state operation at EBR-II. The data have beendigitized at a 2-per-second sampling rate using 2¹⁴ (16,384)observations for each signal of interest.

FIGS. 1-3 illustrate data associated with the preferred spectralfiltering approach as applied to the EBR-II primary pump power signal,which measures the power (in kW) needed to operate the pump. The basicprocedure of FIG. 8 was then followed in the analysis. FIG. 1 shows 136minutes of the original signal as it was digitized at the 2-Hz samplingrate. FIG. 2 shows a Fourier composite constructed from the eight mostprominent harmonics identified in the original signal. The residualfunction, obtained by subtracting the Fourier composite curve from theraw data, is shown in FIG. 3. Periodograms of the raw signal and theresidual function have been computed and are plotted in FIG. 4. Note thepresence of eight depressions in the periodogram of the residualfunction in FIG. 4B, corresponding to the most prominent periodicitiesin the original, unfiltered data. Histograms computed from the rawsignal and the residual function are plotted in FIG. 5. For eachhistogram shown we have superimposed a Gaussian curve (solid line)computed from a purely Gaussian distribution having the same mean andvariance. Comparison of FIG. 5A and 5B provide a clear demonstration ofthe effectiveness of the spectral filtering in reducing asymmetry in thehistogram. Quantitatively, this decreased asymmetry is reflected in adecrease in the skewness (or third moment of the noise) from 0.15 (rawsignal) to 0.10 (residual function).

It should be noted here that selective spectral filtering, which we havedesigned to reduce the consequences of serial correlation in oursequential testing scheme, does not require that the degree ofnonnormality in the data will also be reduced. For many of the signalswe have investigated at EBR-II, the reduction in serial correlation is,however, accompanied by a reduction in the absolute value of theskewness for the residual function.

To quantitatively evaluate the improvement in whiteness effected by thespectral filtering method, we employ the conventional Fisher Kappa whitenoise test. For each time series we compute the Fisher Kappa statisticfrom the defining equation ##EQU11## where 1(ω_(k)) is the PSD function(see Eq. 14) at discrete frequencies ω_(k), and 1(L) signifies thelargest PSD ordinate identified in the stationary time series.

The Kappa statistic is the ratio of the largest PSD ordinate for thesignal to the average ordinate for a PSD computed from a signalcontaminated with pure white noise. For EBR-II the power signal for thepump used in the present example has a κ of 1940 and 68.7 for the rawsignal and the residual function, respectively. Thus, we can say thatthe spectral filtering procedure has reduced the degree of nonwhitenessin the signal by a factor of 28. Strictly speaking, the residualfunction is still not a pure white noise process. The 95% critical valuefor Kappa for a time series with 2¹⁴ observations is 12.6. This meansthat only for computed Kappa statistics lower than 12.6 could we acceptthe null hypothesis that the signal is contaminated by pure white noise.The fact that our residual function is not purely white is reasonable ona physical basis because the complex interplay of mechanisms thatinfluence the stochastic components of a physical process would not beexpected to have a purely white correlation structure. The importantpoint, however, is that the reduction in nonwhiteness effected by thespectral filtering procedure using only the highest eight harmonics inthe raw signal has been found to preserve the pre-specified false alarmand missed alarm probabilities in the SPRT sequential testing procedure(see below). Table I summarizes the computed Fisher Kappa statistics forthirteen EBR-II plant signals that are used in the subject surveillancesystems. In every case the table shows a substantial improvement insignal whiteness.

The complete SPRT technique integrates the spectral decomposition andfiltering process steps described hereinbefore with the known SPRTbinary hypothesis procedure. The process can be illustrativelydemonstrated by application of the SPRT technique to two redundantdelayed neutron detectors (designated DND A and DND B) whose signalswere archived during long-term normal (i.e., undegraded) operation witha steady DN source in EBR-II. For demonstration purposes a SPRT wasdesigned with a false alarm rate, α, of 0.01. Although this value ishigher than we would designate for a production surveillance system, itgives a reasonable frequency of false alarms so that asymptotic valuesof α can be obtained with only tens of thousands of discreteobservations. According to the theory of the SPRT technique, it can beeasily proved that for pure white noise (such as Gaussian),independently distributed processes, α provides an upper bound to theprobability (per observation interval) of obtaining a false alarm--i.e.,obtaining a "data disturbance" annunciation when, in fact, the signalsunder surveillance are undegraded.

FIGS. 6 and 7 illustrate sequences of SPRT results for raw DND signalsand for spectrally-whitened DND signals, respectively. In FIGS. 6A and6B, and 7A and 7B, respectively, are shown the DN signals from detectorsDND-A and DND-B. The steady-state values of the signals have beennormalized to zero.

                  TABLE I                                                         ______________________________________                                        Effectiveness of Spectral Filtering for Measured Plant Signals                               Fisher Kappa Test Statistic                                                   (N=16,384)                                                     Plant Variable I.D.                                                                            Raw Signal Residual Function                                 ______________________________________                                        Pump 1 Power     1940       68.7                                              Pump 2 Power     366        52.2                                              Pump 1 Speed     181        25.6                                              Pump 2 Speed     299        30.9                                              Pump 1 Radial Vibr (top)                                                                       123        67.7                                              Pump 2 Radial Vibr (top)                                                                       155        65.4                                              Pump 1 Radial Vibr (bottom)                                                                    1520       290.0                                             Pump 2 Radial Vibr (bottom)                                                                    1694       80.1                                              DN Monitor A      96        39.4                                              DN Monitor B      81        44.9                                              DN Detector 1     86        36.0                                              DN Detector 2    149        44.1                                              DN Detector 3     13        8.2                                               ______________________________________                                    

Normalization to adjust for differences in calibration factor or viewinggeometry for redundant sensors does not affect the operability of theSPRT. FIGS. 6C and 7C in each figure show pointwise differences ofsignals DND-A and DND-B. It is this difference function that is input tothe SPRT technique. Output from the SPRT method is shown for a250-second segment in FIGS. 6D and 7D.

Interpretation of the SPRT output in FIGS. 6D and 7D is as follows: Whenthe SPRT index reaches a lower threshold, A, one can conclude with a 99%confidence factor that there is no degradation in the sensors. For thisdemonstration A is equal to 4.60, which corresponds to false-alarm andmissed-alarm probabilities of 0.01. As FIGS. 6D and 7D illustrate, eachtime the SPRT output data reaches A, it is reset to zero and thesurveillance continues.

If the SPRT index drifts in the positive direction and exceeds apositive threshold, B, of +4.60, then it can be concluded with a 99%confidence factor that there is degradation in at least one of thesensors. Any triggers of the positive threshold are signified withdiamond symbols in FIGS. 6D and 7D. In this case, since we can certifythat the detectors were functioning properly during the time period oursignals were being archived, any triggers of the positive threshold arefalse alarms.

If we extend sufficiently the surveillance experiment illustrated inFIG. 6D, we can get an asymptotic estimate of the false alarmprobability α. We have performed this exercise using 1000-observationwindows, tracking the frequency of false alarm trips in each window,then repeating the procedure for a total of sixteen independent windowsto get an estimate of the variance on this procedure for evaluating α.The resulting false-alarm frequency for the raw, unfiltered, signals isα=0.07330 with a variance of 0.000075. The very small variance showsthat there would be only a negligible improvement in our estimate byextending the experiment to longer data streams. This value of α issignificantly higher than the design value of α=0.01, and illustratesthe danger of blindly applying a SPRT test technique to signals that maybe contaminated by excessive serial correlation.

The data output shown in FIG. 7D employs the complete SPRT techniqueshown schematically in FIG. 8. When we repeat the foregoing exerciseusing 16 independent 1000-observation windows, we obtain an asymptoticcumulative false-alarm frequency of 0.009142 with a variance of0.000036. This is less than (i.e., more conservative than) the designvalue of α=0.01, as desired.

It will be recalled from the description hereinbefore regarding onepreferred embodiment, we have used the eight most prominent harmonics inthe spectral filtration stage of the SPRT technique. By repeating theforegoing empirical procedure for evaluating the asymptotic values of α,we have found that eight modes are sufficient for the input variablesshown in Table I. Furthermore, by simulating subtle degradation inindividual signals, we have found that the presence of serialcorrelation in raw signals gives rise to excessive missed-alarmprobabilities as well. In this case spectral whitening is equallyeffective in ensuring that pre-specified missed-alarm probabilities arenot exceeded using the SPRT technique.

In another different form of the invention, it is not necessary to havetwo sensor signals to form a difference function. One sensor can providea real signal characteristic of an ongoing process and a recordartificial signal can be generated to allow formation of a differencefunction. Techniques such as an auto regressive moving average (ARMA)methodology can be used to provide the appropriate signal, such as a DClevel signal, a cyclic signal or other predictable signal. Such an ARMAmethod is a well-known procedure for generating artificial signalvalues, and this method can even be used to learn the particular cyclicnature of a process being monitored enabling construction of theartificial signal.

The two signals, one a real sensor signal and the other an artificialsignal, can thus be used in the same manner as described hereinbeforefor two real sensor signals. The difference function Y is then formed,transformations performed and a residual function is determined which isfree of serially correlated noise.

Fourier techniques are very effective in achieving a whitened signal foranalysis, but there are other means to achieve substantially the sameresults using a different analytical methodology. For example,filtration of serial correlation can be accomplished by using theautoregressive moving average (ARMA) method. This ARMA techniqueestimates the specific correlation structure existing between sensorpoints of an industrial process and utilizes this correlation estimateto effectively filter the data sample being evaluated.

A technique has therefore been devised to produce reliable data basesfree from false alarm information which integrates frequency-domainfiltering with sequential testing methodology. This method provides asolution to a problem that is endemic to industrial signal evaluationsurveillance. For example, it is not uncommon for sensors to becomedegraded during service, and faulty signals will be generated. Suchfaulty signals can give rise to false alarms and result in accumulationof a faulted data base intended for use in the future as a reliablesource of information. The subject invention particularly allowsidentification of valid or corrupted data and consequent use of reliabledata base information in analyzing industrial systems. For example, thisinvention would be particularly useful in metereological systems,aeronautical design systems, automative simulation systems or any systemwherein experimental data can be used for modeling or design projects.Further, one can evaluate ongoing slow degradation that evolves over along time period (gradual decalibration bias in a sensor, appearance ofa new radiation source in the presence of a noisy background signal,wear out or buildup of a radial rub in rotating machinery, etc.). Thesystem thus can alert a researcher or operator of the incipience oronset of a disturbance long before it would be apparent to visualinspection of strip chart or CRT signal traces, and well beforeconventional threshold limit checks would be tripped. This permits theresearcher to either have a reliable data base for research use or toactively use the data base to terminate, modify or avoid events thatmight otherwise lie outside technical specification guidelines oravailability goals. Thus, in many cases a user of such a data base cananticipate or schedule corrective actions (sensor replacement orrecalibration; component adjustment, alignment, or rebalancing; etc.) tobe performed during a scheduled system outage.

Another important feature of the technique which distinguishes it fromconventional methods is the built-in quantitative false-alarm andmissed-alarm probabilities. This is quite important in the context ofhigh-risk industrial processes and applications. The invention makes itpossible to apply formal reliability analysis methods to an overallsystem comprising a network of interacting SPRT modules that aresimultaneously monitoring a variety of plan variables. This amenabilityto formal reliability analysis methodology will, for example, greatlyenhance the process of granting approval for nuclear-plant applicationsof the invention, a system that can potentially save a utility millionsof dollars per year per reactor.

While preferred embodiments of the invention have been shown anddescribed, it will be clear to those skilled in the art that variouschanges and modifications can be made without departing from theinvention in its broader aspects as set forth in the claims providedhereinafter.

What is claimed is:
 1. A method of processing at least one data baseobtained from at least one of an industrial process and at least a firstand second sensor for determining fault conditions of datacharacteristic of a process, comprising the steps of:collecting datafrom at least a first and second sensor to redundantly accumulate datafrom at least one physical variable of the industrial process to providea first data signal from said first sensor and a second data signal fromsaid second sensor, each said data signal being characteristic of theone physical variable; obtaining a difference function of the datacharacteristic of the arithmetic difference pairwise between said firstdata signal and said second data signal at each of a plurality ofdifferent times of sensing the one physical variable; obtaining afrequency domain transformation of said first difference function toprocure Fourier coefficients corresponding to Fourier frequencies;generating a composite function over a time domain using the Fouriercoefficients; obtaining a residual function over time by determining thearithmetic difference between the difference function and the compositefunction, the residual function having reduced serially correlatednoise; operating on the residual function using computer means forperforming a statistical analysis technique to determine whether alarmcondition data is present in at least one of the data base from theindustrial process and from the at least first and second sensor, theresidual function including white noise characteristics of anuncorrelated function of reduced skewness relative to the differencefunction and input to the statistical analysis technique; and producingsaid at least one data base having data with identified alarm conditionsassociated therewith, allowing separation of said data with identifiedalarm conditions.
 2. The method described is claim 1 wherein saidcomputer means comprises an artificial intelligence system.
 3. Themethod as defined in claim 1 wherein the residual function furthercomprises reduced Markov dependent noise.
 4. The method as defined inclaim 1 wherein the industrial process data base comprises at least oneof a chemical process data base, a mechanical process data base and anelectrical process data base.
 5. The method as defined in claim 1wherein the step of obtaining Fourier coefficients comprise iterativelydetermining the minimum number of Fourier harmonics able to generate thecomposite function.
 6. The method as defined in claim 1 furtherincluding at least one of the steps of identifying or removing datahaving alarm conditions associated therewith.
 7. A method ofaccumulating a data base with validated information from at least one ofan industrial process and a sensor for determining fault conditionstherein, comprising the steps of:collecting data from at least onesensor to detect at least one physical variable of the industrialprocess to provide a real signal from said one sensor; generating anartificial data signal characteristic of the one physical variable;obtaining a difference function characteristic of the differencepairwise between said real signal and said artificial signal at each ofa plurality of different times of sensing the one physical variable;obtaining a frequency domain transformation of said difference function;generating a composite function data base over a time domain; obtaininga residual function over time by determining the difference between thedifference function and the composite function data base, the residualfunction including white noise characteristics of an uncorrelated signalof reduced skewness compared to the difference function; and operatingon the residual function using a computer means for performing astatistical analysis technique to determine whether alarm condition datais present in at least one of the industrial process and the at leastone sensor, the residual function having said white noisecharacteristics input to the statistical analysis technique forproviding the data base with validated information.
 8. The method asdefined in claim 7 wherein the step of obtaining a frequency domaintransformation comprises performing a Fourier transformation.
 9. Themethod as deemed in claim 7 wherein the steps of obtaining a compositefunction over time comprises performing an autoregressive moving averageanalysis.
 10. The method as deemed in claim 7 further including the stepof determining a difference function for both the artificial signal andthe real signal, as well as a separate pair of real signals.
 11. Themethod as defined in claim 7 wherein the residual function furthercomprises reduced Markov dependent noise.
 12. The method as defined inclaim 8 wherein the step of obtaining a frequency domain transformationcomprises obtaining Fourier coefficients iteratively to determine theminimum number of Fourier harmonics able to generate the compositefunction data base.
 13. A system for accumulating a data base withvalidated signals from data obtained from at least one of an industrialprocess and a sensor for determining a fault condition therein,comprising:first means for providing a first set of data characteristicof at least one physical variable of the industrial process; secondmeans for providing a second set of data calculationally determined andrelated to the one physical variable of the industrial process; thirdmeans for determining a difference function of data characteristic ofthe arithmetic difference pairwise between said first set of data andsaid second set of data at each of a plurality of different times of theone physical variable being sensed; fourth means for obtaining aresidual function of data over time by means for determining thearithmetic difference between the difference function data and thecomposite function data, the residual function data having reducedserially correlated noise; and fifth means for operating on the residualfunction data including a computer means for performing a statisticalanalysis technique and for determining whether corrupted data is presentin at least one of the data obtained from the industrial process and thesensor and with said third means, said fourth means, and said fifthmeans cooperatively providing the residual function data with whitenoise characteristics of an uncorrelated signal of reduced skewnessrelative to the difference function as an input to the statisticalanalysis technique to provide the data base with validated signals. 14.The system as defined in claim 13 further including means for obtaininga frequency domain transformation of said difference function data. 15.The system as defined in claim 13 wherein said computer means comprisesan artificial intelligence system.
 16. The system as defined in claim 13wherein said means for calculationally generating a second set of datacomprises computer means for executing a computer program.
 17. Thesystem as defined in claim 16 wherein the computer program includes anautoregressive moving average procedure.
 18. The system as defined inclaim 13 wherein the system includes at least one pair of sensor datasets.
 19. The system as defined in claim 13 wherein said computer meansexecutes a computer program including a statistical probability ratiotest on the residual function data.
 20. The system as defined in claim13 further including means for at least one of identifying or removingalarm data from the industrial process data and the sensor data.
 21. Amethod of processing at least one data base obtained from at least oneof an industrial process and at least a first and second sensor fordetermining fault conditions of data characteristic of a process,comprising the steps of:collecting data from the at least first andsecond sensor to accumulate comparative data for at least one physicalvariable of the industrial process to provide a first data signal fromsaid first sensor and a second data signal from said second sensor, eachsaid data signal being characteristic of the one physical variable;obtaining a difference function of the data characteristic of thearithmetic difference pairwise between said first data signal and saidsecond data signal at each of a plurality of different times of sensingthe one physical variable; obtaining a frequency domain transformationof said first difference function to procure Fourier coefficientscorresponding to Fourier frequencies; generating a composite functionover a time domain using the Fourier coefficients; obtaining a residualfunction over time by determining the arithmetic difference between thedifference function and the composite function, the residual functionhaving reduced serially correlated noise; operating on the residualfunction using computer means for performing a statistical analysistechnique to determine whether alarm condition data is present in the atleast one data base from the industrial process and the first and secondsensor, the residual function including white noise characteristics ofan uncorrelated function of reduced skewness relative to the differencefunction and input to the statistical analysis technique; and producingsaid at least one data base having data with identified alarm conditionsassociated therewith, allowing separation of said data with identifiedalarm conditions.
 22. The method as defined in claim 21 wherein saidfirst and second sensor measure wear out conditions in machinery.
 23. Asystem for accumulating a data base with validated signals from dataobtained from at least one of an industrial process and a sensor fordetermining a fault condition therein, comprising:first means forproviding a first set of data characteristic of at least one physicalvariable of the industrial process; second means for providing a secondset of data related to the one physical variable of the industrialprocess; third means for determining a difference function of datacharacteristic of the arithmetic difference pairwise between said firstset of data and said second set of data at each of a plurality ofdifferent times of the one physical variable being sensed; means forgenerating composite function data over a time domain; fourth means forobtaining a residual function of data over time by means for determiningthe arithmetic difference between the difference function data and thecomposite function data, the residual function data having reducedserially correlated noise; and fifth means for operating on the residualfunction data including a computer means for performing a statisticalanalysis technique and for determining whether degraded data is presentin at least one of the data from the industrial process and from thesensor and with said third means, said fourth means, and said fifthmeans cooperatively providing the residual function data with whitenoise characteristics of an uncorrelated signal of reduced skewnessrelative to the difference function as an input to the statisticalanalysis technique to provide the data base with validated signals.